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A218360
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Minimal order of degree-n irreducible polynomials over GF(13).
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4
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1, 7, 9, 5, 30941, 63, 5229043, 32, 27, 11, 23, 45, 53, 29, 4651, 64, 103, 19, 12865927, 25, 43, 161, 1381, 288, 701, 371, 81, 145, 1973, 31, 311, 128, 207, 721, 211, 37, 1481, 90061489, 79, 41, 6740847065723, 261, 119627, 115, 181, 47, 183959, 576, 1667, 101
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OFFSET
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1,2
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COMMENTS
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a(n) < 13^n.
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LINKS
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Max Alekseyev, Table of n, a(n) for n = 1..416
Eric Weisstein's World of Mathematics, Irreducible Polynomial
Eric Weisstein's World of Mathematics, Polynomial Order
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FORMULA
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a(n) = min(M(n)) with M(n) = {d : d|(13^n-1)} \ U(n-1) and U(n) = M(n) union U(n-1) for n>0, U(0) = {}.
a(n) = A218337(n,1) = A213224(n,6).
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MAPLE
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with(numtheory):
M:= proc(n) M(n):= divisors(13^n-1) minus U(n-1) end:
U:= proc(n) U(n):= `if`(n=0, {}, M(n) union U(n-1)) end:
a:= n-> min(M(n)[]):
seq(a(n), n=1..33);
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MATHEMATICA
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M[n_] := M[n] = Divisors[13^n - 1]~Complement~U[n - 1];
U[n_] := U[n] = If[n == 0, {}, M[n]~Union~U[n - 1]];
a[n_] := Min[M[n]];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 24 2022, after Alois P. Heinz *)
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CROSSREFS
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Cf. A213224, A218337.
Sequence in context: A132715 A154910 A063603 * A020788 A198921 A099877
Adjacent sequences: A218357 A218358 A218359 * A218361 A218362 A218363
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 27 2012
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STATUS
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approved
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